Stability Analysis of a Dynamical Model Representing Gene Regulatory Networks

Abstract

Abstract:In this paper we perform stability analysis of a class of cyclic biological processes involving time delayed feedback. More precisely, we analyze the genetic regulatory network having nonlinearities with negative Schwarzian derivatives. We derive a set of conditions implying global stability of the genetic regulatory network under positive feedback. As a special case, we also consider homogenous genetic regulatory networks and obtain an appropriate stability condition which depends only on the parameters of the nonlinearity function.

On the analysis of a dynamical model representing gene regulatory networks under negative feedback

“…In this work, GRNs are considered; these are modeled as cyclic nonlinear dynamical systems with time delayed feedback. The negative feedback case is studied here; for the positive feedback case, see [19,23]. The nonlinearity functions are assumed to have negative Schwarzian derivatives.…”

“…Also note that to have negative feedback, we should have odd number of interactions between genes. If n is even, the system is under positive feedback, which is studied in [23]. That is, n should be an odd number.…”